Linear Algebra Fundamentals for Machine Learning
Chapter 1: Chapter 1: The Building Blocks: Scalars, Vectors, and Matrices
Why Linear Algebra for Machine Learning?
Scalars: The Simplest Objects
Vectors: Points in Space
Matrices: Organizing Data in Grids
Setting Up Your Python Environment
Hands-On Practical: Creating Vectors and Matrices with NumPy
Chapter 2: Chapter 2: Working with Vectors
Vector Addition and Subtraction
Scalar Multiplication
The Dot Product
Vector Norms: Measuring Length
Orthogonal Vectors
Hands-On Practical: Vector Operations in NumPy
Chapter 3: Chapter 3: Working with Matrices
Matrix Addition and Subtraction
Matrix-Scalar Multiplication
Matrix-Vector Multiplication
Matrix-Matrix Multiplication
The Matrix Transpose
Special Types of Matrices
Hands-On Practical: Matrix Operations in NumPy
Chapter 4: Chapter 4: Systems of Linear Equations
Representing Equations in Matrix Form (Ax = b)
The Identity Matrix
The Matrix Inverse
Determinants and Invertibility
Singular vs. Non-Singular Matrices
Hands-On Practical: Solving Systems with NumPy
Chapter 5: Chapter 5: Eigenvalues and Eigenvectors
Matrices as Linear Transformations
Defining Eigenvalues and Eigenvectors
Geometric Interpretation
The Characteristic Equation
Hands-On Practical: Finding Eigenvalues with NumPy
Chapter 6: Chapter 6: Connecting to Machine Learning
Data Representation for Models
Linear Regression as a Matrix Problem
Dimensionality Reduction with PCA
Measuring Similarity with Dot Products
Practice: Data Manipulation with NumPy
The Matrix Inverse
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- Introduction to Linear Algebra, Gilbert Strang, 2016 (Wellesley-Cambridge Press) - A fundamental textbook for a comprehensive understanding of linear algebra basics, including matrix operations, inverses, and solving systems of equations.
- 18.06SC Linear Algebra, Gilbert Strang, 2011 (MIT OpenCourseWare) - Provides video lectures and comprehensive course materials on linear algebra, directly covering matrix inverses and their role in solving $Ax=b$.
- Deep Learning, Ian Goodfellow, Yoshua Bengio, Aaron Courville, 2016 (MIT Press) - Chapter 2, 'Linear Algebra,' offers an applied perspective on concepts essential for machine learning, including matrix inverses and solving systems of equations.
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